An alternate scheme for linogram image reconstruction, which is more logical from the viewpoint of its applicability to MRI data, is presented here. As a result, an intermediate step for this method, the direct Fourier method (DFM) gives the same results as the earlier developed general reconstruction algorithm labeled as the linogram method (LM). However, the two differ in the pathways taken to the solution. As a result, an intermediate step for DFM corresponds directly with the geometry of linogram data collected for MRI, in contrast to the LM reconstruction. The two reconstruction methods are delineated within the context of MRI data reconstruction, and applied to reconstruct images from linogram spin-echo data of a physical phantom, obtained on a clinical 1.5 T scanner.